To solve this problem, we can set up a system of equations based on the given information.
Let's use x to represent the distance traveled at 100 km/h and y to represent the distance traveled at 80 km/h.
According to the problem, Nicolas drove a total distance of 500 km and took 5.5 hours.
We know that the time taken to travel a certain distance is equal to the distance divided by the speed.
So, we can write two equations based on the time and distance traveled at each speed:
Equation 1: x/100 + y/80 = 5.5 (time equation)
Equation 2: x + y = 500 (distance equation)
Now, we can solve this system of equations to find the values of x and y.
Multiplying Equation 1 by 400 to eliminate the fractions, we get:400(x/100) + 400(y/80) = 400(5.5)
4x + 5y = 2200
Next, we can use Equation 2:
x + y = 500
We can solve this system of equations using any method, such as substitution or elimination.
Let's solve it by elimination. Multiply Equation 2 by 4 to make the coefficients of x the same:4(x + y) = 4(500)
4x + 4y = 2000
Now, subtract the equation 4x + 4y = 2000 from the equation 4x + 5y = 2200:
4x + 5y - (4x + 4y) = 2200 - 2000
y = 200
Substitute the value of y back into Equation 2 to find x:
x + 200 = 500
x = 300
Therefore, Nicolas drove 300 km at 100 km/h and 200 km at 80 km/h.
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Triangle CAT has vertices C (2,3), A(-2,6) and T(-1,-4). A translation maps the point A to A' (-1,4). What are the coordinates of C' under this translation?
A. (1, -3)
B. (3, 1)
C. (1, 8)
D. (-8, 1)
you add 1 and subtracted 2
so 2 + 1 = 3
3 - 2 = 1
answer: b. (3, 1)
what is the formula of volume
Answer:
length × width × height.
Step-by-step explanation:
Answer:
length × width × height
Step-by-step explanation:
That is the standard formula for a rectangular shape
Write the coefficients of:
xin 3xy + 8y - Oy
(11) 5 in 61-57'n + 8p
(ii) z'in 3xy +42-64
(iv) yz in 3x - 5yx
Step-by-step explanation:
Here x coefficients are 3y + 8y - OyHere 5 coefficients are 61-7'n + 8pHere z coefficients are 0Here yz coefficients are 0Find the missing length?
A. 18in
B. 6in
C. 2in
D. 36in
Answer:
B. 6in
Step-by-step explanation:
We can use the Pythagorean theorem [ a² + b² = c² ] to find the missing side.
8² + b² = 10²
64 + b² = 100
b² = 36
b = 6
Best of Luck!
What is m = -13/6.5 simplified?
please help explain how u got the answer marking brainlist giving all my points 200 points
Answer:
v = -35
Step-by-step explanation:
-4 -31= -35 which leaves V. so v=-35
Answer:
I think that the is -27
Step-by-step explanation: 32 - (-27) = -4
Plz help due tomorrow
Answer:
A) x is greater than or equal to 4.50
Step-by-step explanation:
the price has to be at least 4.50 so it could be 4.50 or it could be greater than 4.50. Hope this helped.
Three rabbits can eat five carrots in four minutes. How long does it take four rabbits to eat 15 carrots?
Answer:
12
Step-by-step explanation:
15/5=3
3x4=12
Which graph represents a proportional relationship? (quickly please :)
Answer:
the first one
Step-by-step explanation:
a proportional graph has to go through the origin (0,0) and the first one is the only one that does
Herbert is decorating the bulletin board at school.The bulletin board is 7 ft by 11 ft.He decides to add a black border.What is the length of the border needed?
Answer:
36 feets
Step-by-step explanation:
The dimension of bulletin board = 7 feets by 11 feets
Bulletin boards are shaped as a rectangle :
To add a black border ; two of the sides will be of length 7 feets (length) while the other 2 will be of 11 feets (width) each or vice-versa
However, total Lenght of black border :
(11 * 2) + (7 * 2)
22 + 14
= 36 feets
Find the area of the regular octagon.
Answer:
3*4
=12 sq. cm
= 12 cm²
Answer:
48cm^{2}
Step-by-step explanation:
[tex]A=4ah=4*4*3=48 cm^{2}[/tex]
what is not a composite number out of 2 4 6 8
Answer:
2
Step-by-step explanation:
2 has the factors 2 and 1 while the others have:
4- 4, 2,1
6- 6, 3, 2, 1
8- 8, 4, 2, 1
Write the equations of the line that passes through the point 4,3) and is perpendicular to the line y=2x−4 . Write the equation in slope-intercept form.
Answer:
y = -¹/₂x + 5Step-by-step explanation:
The product of slopes of perpendicular lines is -1
y = 2x − 4 ⇒ m₁ = 2
m₁m₂ = -1
2m₂ = -1
m₂ = -¹/₂
The Point-Slope form of equation of a line with slope of "m" and passing through point (x₁, y₁) is: y - y₁ = m(x - x₁)
m = -¹/₂
(4, 3) ⇒ x₁ = 4, y₁ = 3
So the equation in point-slope form:
y - 3 = -¹/₂(x - 4)
Therefore:
y - 3 = -¹/₂x + 2
y = -¹/₂x + 2 + 3
y = -¹/₂x + 5Determine the slope and the y-intercept: y = 3x - 1
Answer:
Slope is 3
y - intercept is -1
Answer:
slope = 3, y- intercept is - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x - 1 ← is in slope- intercept form
with slope m = 3 and y- intercept c = - 1
PLS HELPPPP I NEED THIS GRADE PLSSSSS...The length of yarn needed to knit one hat is half the length of yarn that is needed to knit a scarf. It takes three times as much yarn to knit a
child's sweater as it does to knit one hat.
a. If It takes 400 yards of yarn to knit a scarf, how much yarn is needed to knit a child's sweater? Use tape diagrams and equations to solve
the problem. Use paper to show your work. Let h represent the number of yards of yarn needed to knit a hat.
It will take yards of yarn to knit a child's sweater.
b. How many total yards of yarn will be needed to knit a hat, a scarf, and a child's sweater?
It will take yards of yarn to knit a hat, a scarf, and a child's sweater
Answer:
A: 2,400 yards is needed for the child's sweater
you would take 400*2 to get the amount of yarn for the hat (800)take 800 (value of the hat) * 3 (the sweater uses three times as much yarn than the hat) = 2,400.B: HAT: 800 yards
SCARF: 400 yards
SWEATER: 2,400 yards
we already have all of the values present from the first part of the problem, so we would just plug those in for the correct thing.Step-by-step explanation:
i really hope this helped! if it did please give me brainliest.
100 POINTS IF YOU HELP MEE !! AND ILL GIVE BRAINLISTT !! Complete each statement with the number used to create an equivalent fraction. Multiply to by in both the numerator and denominator to get Multiply { by in both the numerator and denominator to get 16 Multiply by in both the numerator and denominator to get 24 Multiply 1 by in both the numerator and denominator to get 16
Answer:
Step-by-step explanation:
8/8 5/5
A bricklayer lays 1200 bricks in an average 8-hour day. How many bricks does he lay in a 40-hour week?
The number of bricks that the bricklayer can lay in a 40-hour week is 6000 bricks.
Let the number of bricks that the bricklayer can lay in a 40-hour week be represented by x.
Based on the information given in the question, the equation to solve the question will be:
8/40 = 1200/x
Cross multiply
8 × x = 1200 × 40
x = (1200 × 40) / 8
x = 1200 × 5
x = 6000
Therefore, the number of bricks that the bricklayer can lay in a 40-hour week is 6000 bricks.
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9514 1404 393
Answer:
(0, 0) 2, 4, 5
(-1, -1) 1, 2, 4, 5
(2, -1) 1, 2, 4, 5
(-2, 2) 2, 4
Step-by-step explanation:
The graph shows the solution sets of the inequalities. Each inequality is graphed in a different color to aid identification of the solution areas.
The purple area, x + 3y ≥ 6, does not contain any of the given points.
The inequalities satisfied by the given points are listed above.
PLS PLS PLS PLS HELP ME
Exponents work the same way on bases that are _[blank A]_ as they do on bases that are numbers.
When a variable has an exponent, the exponent tells you how many times the variable is _[blank B]_ by itself.
In order to make a negative exponent positive, you must take the _[blank C]_ of the base.
A variable raised to the power of _[blank D]_ is always equal to 1.
Match each blank with the correct item that fills in that blank.
multiplied
0
exponents
reciprocal
1
added
variables
opposite
A - variables
B - multiplied
C - reciprocal?
D - 0
//
I'm not too sure about C. it can either be the reciprocal or the opposite.
If the points at (-4, 3) and (2, 3) are reflected over the x-axis to create two new points, what shape can be formed by the four points? Select the most precise description of the shape.
square
rectangle
triangle
trapezoid
Answer:
square
Step-by-step explanation:
Carl is deriving the quadratic equation by completing the square. His work at one of the steps is shown. x + b/na = + or - b^2-4ac. Carl is not sure what the value of n is. What value should he use to continue deriving the quadratic equation correctly? A. 1 B. 2 C. 3 D. 4
Answer:
the correct option is B. 2
Step-by-step explanation:
As given,
x + [tex]\frac{b}{na}[/tex] = ± √b²-4ac
⇒x = -[tex]\frac{b}{na}[/tex] ± √b²-4ac
As e know that the quadratic formula is
x = [tex]\frac{-b + or - \sqrt{b^{2} - 4ac } }{2a}[/tex]
So , by comparing with the formula
we get
n = 2
So, the correct option is B. 2
Christina earned $510 working part-time at the movie theater. Of her paycheck, 1/ 4 pays for car insurance, 1/ 3 for gas, and 20% for miscellaneous expenses. The remaining amount of her paycheck is divided equally for entertainment and savings. How much does Christina spend each month on entertainment?
Answer:
$55.15
Step-by-step explanation:
1/4 of 510 = 127.5
1/3 of 510 = 170
20% of 510 = 102
510-(127.7+102+170)=510-399.7=110.3
110.3/2=55.15
hope this helps
Calculate the value of this expression by writing the decimal factors as fractions, then writing their product as a decimal. Show your reasoning. (0.3)⋅(0.2)
Answer:
(3/10)(2/10) = 6/100 = 0.06
What is a perfect square? Why is [tex]x^{2} + 8x +16[/tex] a perfect square?
Answer:
It is a perfect square. Explanation below.
Explanation:
Perfect squares are of the form
(
a
+
b
)
2
=
a
2
+
2
a
b
+
b
2
. In polynomials of x, the a-term is always x.(
(
x
+
c
)
2
=
x
2
+
2
c
x
+
c
2
)
x
2
+
8
x
+
16
is the given trinomial. Notice that the first term and the constant are both perfect squares:
x
2
is the square of x and 16 is the square of 4.
So we find that the first and last terms correspond to our expansion. Now we must check if the middle term,
8
x
is of the form
2
c
x
.
The middle term is twice the constant times x, so it is
2
×
4
×
x
=
8
x
.
Okay, we found out that the trinomial is of the form
(
x
+
c
)
2
, where
x
=
x
and
c
=
4
.
Let us rewrite it as
x
2
+
8
x
+
16
=
(
x
+
4
)
2
. Now we can say it is a perfect square, as it is the square of
(
x
+
4
)
.
Round the 136.501 to the whole number.
Answer:
137
Step-by-step explanation:
137 because when it's .5 or higher you round up
How would I solve this?
Answer:
2.74747741945462
Step-by-step explanation:
i know its long but i think it is correct!:)
Jim rides the bus to and from school each day. A one-way trip is 8.12 kilometers. How many kilometers does he travel in 3 days?
Answer:
48.72 km in 3 days.
Step-by-step explanation:
Given that,
A one-way trip is 8.12 kilometers.
We need to find the distance he travel in 3 days.
The distance traveled by Jim in one day to the bus and from school = 2(8.12) = 16.24 km
Distance traveled in 3 days = 3(16.24)
= 48.72 km
Hence, he will cover 48.72 km in 3 days.
I NEED THIS RN AS FAST AS POSSIBLE! Your teacher decides to split the class into four equal groups with no more than five students in each group. that represents the number of students in the class.
Answer:
option 1 i think
Step-by-step explanation:
imma just take these 5 points back
Expanded form of 5*10^-9
Answer:
5,000 + 300 + 20 + 5 = 5,325
Step-by-step explanation:
what is the value of a + b(4c + 2a)?
Answer:
Step-by-step explanation:
You can't find an exact value, but you can find an simpler expression by using the distributive property.
a + 4bc + 2ab
And that is as much as it can be reduced.